I have read from multiple threads that you recommend fitting individual processes before fitting parallel process GMM. I was wondering what information we could get from individual ones for the parallel modelling. Do the individual ones determine whether parallel process is appropriate?

Could you talk more about this topic? What are the scenarios that parallel process does not fit the data well? for example, if individual process and parallel one differ a lot, does it indicate that parallel process does not fit the data? ......

If the individual process models fit well and the parallel process model does not, it is misspecified in some way. One possibility is that you may need residual covariances across processes at each time point.

Do you have any example code for setting residual covariances across processes at each time point? If not, could you give a simple example, using the following setting? For example, I have 4 time points, how should we specify residual covariance for %c#1%?